NDA2020MathematicsBasics of MathematicsActual
If x= _c(a b), y= _a(b c), z= _b(c a) , then which of the following is correct?
Options
- Ax y z=1
- Bx+y+z=1
- C(1+x)⁻¹+(1+y)⁻¹+(1+z)⁻¹=1
- D(1+x)⁻²+(1+y)⁻²+(1+z)⁻²=1
Correct answer
C. (1+x)⁻¹+(1+y)⁻¹+(1+z)⁻¹=1
Step-by-step solution
aligned 1+x & = _c(a b)+1 & = _c(a b)+ _c c= _c(a b c) (1+x)⁻¹ & = 1 _c(a b c) = _ (a b c) c aligned (1+x)⁻¹= 1 _c(a b c) = _ (a b c) c Similarly, (1+y)⁻¹= _ (a b c) a and (1+z)⁻¹= _ (a b c) b Now, (1+x)⁻¹+(1+y)⁻¹+(1+z)⁻¹ aligned & = _ (a b c) c+ _ (a b c) a+ _ (a b c) b & = _ (a b c) (c a b)=1 aligned